Why does the coin-flip mechanism work for a yes/no question but break down for open-ended text like "Describe how you use AI"?

Yes/no has a small fixed outcome space and known sensitivity, so noise can be added and removed mathematically; free text is unbounded, so you "can't just flip coins" on it.

The coin flip works because the question is:

• Binary (YES/NO) — a fixed, two-option outcome space.
• Known sensitivity — one person changes the count by exactly ±1.
• Compensable — you can mathematically remove the noise in aggregate.

An open-ended question ("describe in a paragraph…") has unbounded answers and a complex semantic space — you can't enumerate outcomes or calibrate noise the same way. This is exactly the problem with applying DP to LLMs, which produce unbounded text: there's no clean "±1" to mask, so the coin-flip trick simply has nothing to flip.

Tip: DP loves questions with a small, well-defined answer space and bounded per-person influence. The further you get from that, the harder DP becomes.